-Use bows and magic for long range on horses, and swipe with weapons from the horse. Some weapons would swipe faster while others would hit harder. So weapon characteristics on foot would be the same on the horse.
-Return weapons like spears and halberds that were present before Oblivion. Aim it at the person on the horse and knock him off, making him take additional damage and the horse will run for a bit and maybe come back, or at the horse and kill the horse but the person doesn't take any damage.
Suggest anything more that would make horse combat tactical, intense, and of course possible in TES or suggest why it can't happen.